Colorimetry has long been recognized as a complex science. In general, it has been found possible and convenient to represent color stimuli vectors in a three-dimensional space, called tristimulus space. Essentially, as defined in 1931 by the Commission Internationale L'Eclairage (CIE), three primary colors (X, Y, Z) can be combined to define all light sensations we experience with our eyes (that is, the color matching properties of an ideal trichromatic observer defined by specifying three independent functions of wavelength that are identified with the ideal observer's color matching functions form an international standard for specifying color). The fundamentals of such three-dimensional constructs are discussed in the literature, such as Principles of Color Technology, by Billmeyer and Saltzman, published by John Wiley & Sons, Inc., NY, copyright 1981 (2nd. ed.) and Color Science: Concepts and Methods, Quantitative Data and Formulae, by Wyszecki and Stiles, published John Wiley & Sons, Inc., copyright 1982 (2d ed.), incorporated herein by reference in pertinent parts, particularly pages 119-130.
Trichromatic model systems--such as red, green, blue (RGB); cyan, magenta, yellow (CMY); hue, saturation, value (HSV); hue, lightness, saturation (HLS); luminance, red-yellow scale, green-blue scale (La*b*); luminance, red-green scale, yellow-blue scale (Luv); YIQ used in commercial color television broadcasting; and the like--provide alternatives for the system designer. See such works as Fundamentals of Interactive Computer Graphics, by Foley and Van Dam, Addison-Wesley Publishing Company, incorporated herein by reference in pertinent parts, particularly pages 606-621, describing a variety of tri-variable color models.
Color transformation between model systems in digital data processing presents many problems to the original equipment manufacturer. The translation of data from one system to another system is difficult because the relationship between the systems are generally non-linear. Therefore, a crucial problem is the maintaining of color integrity between an original image from an input device (such as a color scanner, CRT display, digital camera, computer software/firmware generation, and the like) and a translated copy at an output device (such as a CRT display, color laser printer, color ink-jet printer, and the like).
For example, computer artists want the ability to create a color image on a computer video and have a printer provide the same color in hard copy. Or, an original color photograph may be digitized with a scanner; resultant data may be transformed for display on a video monitor or reproduced as a hard copy by a laser, ink-jet or thermal transfer printer. As discussed in the reference materials cited, colors can be constructed as renderings of the additive primary colors, red, green, and blue (RGB), or of the subtractive primary colors, cyan, magenta, yellow and black (CMYK). A transformation may require going from an RGB color space, for example, a computer video monitor, to a CMYK color space, for example, a laser printer hard copy. A transformation from one color space to another requires complex, non-linear computations in multiple dimensions. Some transform operations could be accomplished through matrix multiplication.
However, a difficulty in this method of color space conversion results from imperfections in the dyes, phosphors, and toners used for the production of the colors. An additional complication is that different types of media produce different color responses from printing with the same mixes of colorants. As a result, a purely mathematical color space conversion method does not provide acceptable color reproduction.
It has been recognized that superior results in color space conversion are obtained using a look up table scheme based upon a set of empirically derived values. Typically the RGB color space used for video displays use eight bits to represent each of the primary colors, red, green, and blue. Therefore, twenty four bits are required to represent each picture element. With this resolution, the RGB color space would consist of 2.sup.24 or 16,777,216 colors. Performing a color space conversion from each of these points in the RGB color space to generate the four CMYK (to maintain black color purity in printing, a separate black is usually provided rather than printing with all three of cyan, magenta, and yellow colorants to generate what is commonly known as process black) color space components would require a look-up table with 4.times.2.sup.24 or 67,108,864 bytes of data. The empirical construction of a look-up table with this number of entries is too costly.
In making the transform from one color space to another, a number of interpolation schemes well known in the field of color space conversion may be employed. Methods of performing color space conversion using trilinear interpolation, prism interpolation, and tetrahedral interpolation are disclosed in the published article PERFORMING COLOR SPACE CONVERSIONS WITH THREE DIMENSIONAL LINEAR INTERPOLATION, JOURNAL OF ELECTRONIC IMAGING, July 1995 Vol. 4(3), the disclosure of which is incorporated herein by reference. U.S. Pat. No. 3, 893,166 (the disclosure of which is incorporated herein by reference), issued to Pugsley, discloses a scheme for translation between color spaces which uses a look-up table to access values used in an interpolation.
Conversion of large amounts of data between color spaces, such as is required for color printing, is a time consuming operation using the prior art methods of interpolation. The use of the computationally intensive prior art methods of interpolation for the color space conversion process makes high rates of data throughput difficult to achieve. A need exists for an interpolation method and interpolation apparatus that will enable a reduction in the computations required for performing a conversion between color spaces.